I used to compete at dressage, and nothing compares to the terrifyingness of that. It's just you, sitting on half a tonne of potential death or serious injury, being judged both officially and unofficially, against criteria that are both technical and subjective, with absolutely nobody to bail you out and nobody else to blame. On the plus side, you get one hell of an adrenaline rush!
I rarely get stage fright when I play drums, but when I do I have two strategies, both of which involve self-deception. In the first place I make myself smile (the last time, a few weeks ago at my most important gig to date, one of my chickens had just laid her first-ever egg, greeny-blue in colour, and I was so chuffed to bits I couldn't help grinning every time I thought about it); in the second place, I make myself play with conviction. This then gives me genuine confidence, which makes me play better, which makes me smile, which makes me play with more confidence ... it's all good. And of course I have the safety net of my bandmates, which is a great feeling.